A dynamic model of lithium-iron-phosphate (LiFePO4) battery model for vehicle application was setup based on the measurement of its AC impedance by an Electrochemical Impedance Spectroscopy device. According to literature survey, the Randle equivalent circuit seems to be an appropriate one to fit the impedance Nyquist plot of most kind of batteries; however, in this research, a new circuit was suggested to better the fitting accuracy especially at low frequency where batteries often work at in hybrid electric vehicles (HEVs) application. In addition, methods to determine the state of charge (SOC), one of the most important parameters in battery management systems (BMS), were reviewed and a typical ampere-hour counting method, the most common methods, was employed for comparison. The research results show that the electromotive force of the battery has linear relationship with the SOC, so it could give additional information to calibrate the SOC estimation. Most of parameters of the equivalent circuit were interpolated by linear relationship with the SOC.
In order to implement this lithium-ion battery model in HEVs, the frequency domain of the battery impedance was converted into time domain by inverse Laplace transform. Sine the suggested equivalent circuit includes two constant phase elements (CPEs), the approximation is needed here for the converting procedure. So that, the CPE elements were replaced by two basic electrical components: a resistor and a capacitor in parallel. The results show that when lithium ion battery is utilized in vehicle applications, the internal resistance and impedance cannot be neglected; and they affect not only the output voltage of the battery but also the power of the whole system

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